- Email: [email protected]
Dynamic behaviour of pulsed magnets
Dynamic behaviour of pulsed magnets* T. Onishi, H. Tateishi and H. N o m u r a Electrotechnical Laboratory, 1-1-4 Umezono, Tukuba-city, Ibaraki 305, Japan Repetitive pulse operations of 3 MJ pulsed magnet are described. It shows stable performances against 1000 times of pulse operations at Iop/I c ~ 0.75 on the load line and 3.6 T s -1. The evacuation of gas evaporated due to a.c~ losses are considered from viewpoints of flow velocity of the bubbles and the measurements of evaporated gas. A consideration of thermal properties of liquid nitrogen cooled coil is also described.
Keywords: superconducting magnets; pulsed magnets; repetitive cycling
Pulsed superconducting magnets have been developed for applications to fusion reactors, pulsed energy storage equipments, and so on 1-3. It is essentially important to improve the reliability of withstanding repetitive cycles of pulse operations and the duty cycles in order to make them fit for practical use. However, repetitive operations of magnets have not been studied so far from the viewpoint of fatique. It is also important to consider dynamic behaviour of evaporated gas from the viewpoint of duty cycle. In the present paper, the fatigue properties and helium gas behaviour evaporated due to a.c. losses of the 3 MJ pulsed magnet will be discussed.
the 12 double pancake coils are stacked, it is precompressed by about 400 tons, and then fastened with 16 tie rods. The main parameters of the magnet are listed in Table 1. Strain gauges are attached on the surface of the outer support bands of the central and both end pancake coils of the magnet. Those are schematically shown in Figure 5. Three strain gauges are attached separating each other by 120°. CuNi-clad strand (#O~n).
CuNi ~ ~ " " ~ b a s i c
3 MJ pulsed magnet
strand
Nbli
Structure a n d parameters
The conductor used is a multistage twisted cable as shown in Figure 1. A Normex tape (0.5mm thick, 7 mm wide) is wound on the final cable spirally at an interval of 6 mm. The insulated cable is co-wound with the insulated stainless steel strap with approximately the same width as the cable in a double pancake fashion. A schematic illustration of a completed double pancake coil is shown in Figure 2, and a photograph in Figure 3. The glass fibre reinforced plastic (GFRP) spacer (4 mm thick) is interleaved between the single pancake coils. 3 MJ magnet is fabricated by using 12 double pancake coils. The spacers between the coils are 8 mm thick GFRP. The 100 spacers are assembled in a radial manner on the surface of the windings. The ratio of the spacer width and gap between the spacers is designed to be 2:1. Liquidbubble separating plates with the slope of 3° from horizontal are inserted in the gap as shown in Figure 4. Therefore, the helium bubble will not rise to the upward coils but will be evacuated radially along the plate. After
*Paper presented at the Seminar on Basic Mechanisms of Helium Heat Transfer and Related Stability of Superconducting Magnets, Fukuoka, Japan, 29 August-2 September 1988
evel
K (
level
cable
Figure 1
Schematic of cable cross section
0011-2275/89/060659-05 $03.00 © 1989 8utterworth & Co (Publishers) Ltd
Cryogenics 1989 Vol 29 June
659
Dynamic behaviour of pulsed magnets: T. Onishi et al. He bubble r~
(A-A) Bubble-Sepotoling Double Pancake ~
Spacer
Bubble-llquid separating plate
Figure 4 Axial Suppotl PIole
•2 0 0
mm
430 mm
.I
.
.
.
.
Bubble-liquid separc:ting plate
.
Illustration of liquid-bubble separating plate
,0.4 -V
Oul*r ~porI Bond
.I
Figure 2 Double pancake coil structure.Arrows show flow pattern of helium bubbles
Figure 3
,~ ~'="
f
capacity of the power supply. The load line and operating currents are shown in Figure 6.
Fatigue tests• 3 MJ magnet was operated pulsively in bipolar field sweep modes 4. A typical current waveform is shown in Figure 7. These operations were repeated and the total number of operations amounted to 1000 times in all by regarding one operation as an operation from 0 to a peak current and then to 0. During the repetitive pulse operations, the strains of the windings and the total counts of AE signal were measured. The number of the AE signals were summed up from all the AE sensors (44 sensors) which were attached at the end part (near the outermost turn of the windings) of the spacers between the double pancake coils. The results are shown in Figures 8 and 9. Those figures show that any change of strains did not occur up to 1000 times of pulse operations and the AE counts gradually decreased. The reduction of the total AE counts means that the dominant part of the AE in the present magnet came from the wire motions and accordingly they gradually decreased with increasing repetitive pulse operations. Therefore, the rigidity of the windings is supposed to be improved during the repetitive pulse operations up to 1000 times of operations at least. A maximum strain of approximately 200 p.p.m, was obtained, which was consistent with calculation.
Photograph of double pancake coil
•
ST- 1-3
,;U2/I Table 1
Parameters of 3 MJ pulsed magnet
Coil Winding i.d. Winding o.d. Winding height Total turns Inductance lop Gap,coil BM
12 double pancakes 400 mm 860 mm 625 mm 792 0.2 Henry 5500 A 30.3 A mm -2 6.6T
]:::::::::lt_ . . . . . ] i 1 ~
r'
l .... J~| -
/ll::i
,.%
"I
;I----ill
II]::==:l
~
t~ !
Test results Firstly, the magnet was operated at a low rate of change of magnetic field and generated a maximum field of 6.6 T on the windings at 5500 A without any quenches. Then, in a pulse operation the magnetic fields of about 6.5 T and 6 T were generated at 2.2 T s- x and 4 T s- ~, respectively. These operating currents were limited by the
660
Cryogenics 1989 Vol 29 J u n e
•
30mm 400
mm
922 mm I 0 0 0 mm Figure 5
Position of strain gauges
~/
~'
Ch
Dynamic behaviour of pulsed magnets: T. Onishi et al. 3 MJ Pulsed Magnet 10 200t>~tr~e__o_....~°"~o--...tr.o
Pulse Operation
"
/' 5400 A L 6.48T ~ 2.2Z/sec ~
~
~ BM "t , ~
/ 4950 A ( 5.94T ~ / X k4T/sec-/ /
~
.71
~ ~ -~.
. . . .
/
--
--
~ ST6-2 ~ ST1-3 ~ ST1-1 "-- ST1-2
_
~"-D-2
O
"
I m
5500A(DC) 6.6T
--
~
~
f
\
I
/
I I
/ 3
100
~
'-- ST6-3
,-- SS-1 D-3 .1,42-- -,o-.,~>._o,__0.~_~,__o._I~ ..~ D--4
oJ "--"~-.o,- g.- "~"
RepetitivePulse
Operation
--I00~
~.. ~
,o-- ~. ~- ~
"°'--'°'---o---.--o- "~".o
SB-1
2 ._
o ~ . . . ,,----'----~ .4-. . -~. . . 4,--.,4. . . 4-. . .-~--~-~ ,---SB-11
1
0
0
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
-200
B (T) Figure
< ~J
= E
6
L o a d line a n d o p e r a t i n g c u r r e n t of 3 M J m a g n e t
, MJ•magnet
5910 A(4.54 MJ)
6 5 4 3
t
I
-300 500
>
MJ
n
Figure +4
8
12.09 MJ) 0
1
2
3
4
8
1000
Strains
versus
pulse operations
E
"~
5
\
•
-2
~
-4
~
operation
"1
I
I
T
X
6
Typical current waveform of a bipolar field sweep
-
\
Time (s) 7
900
E Q3
o
0
/
800
m
+2
,agnet
/
700
Number of Pulse Operations
A
<
2
Figure
600
I
,¢ O x E
Thermal characteristics. The evaporated gas due to a.c. losses was measured by a mass flow meter at room temperature• A typical result is shown in Figure 10 which was obtained against a pulse operation (0--* 5.9 T - - , 0 at 4 T s - ~). The mass flow of evaporated gas exists for more than 200 s. As will be discussed later, the evaporated gas will be evacuated in about 2 s when it will be in the form of slug flow, while it takes a period roughly in the order of 100 s for evacuation in case of a very fine sphere of, for example, 10#m in diameter. This indicates that the long period of time required for evacuation shown in Figure 11 may be in part caused by the existence of gas in the form of a very fine sphere. Another reason can be explained by the thermal relaxation time of gas in the cryostat.
LU
< o
t-
r •
10 Figure
9
102
10 3
. t ....
Pulse operation Times Total AE counts v e r s u s pulse operation times
Cryogenics 1989 Vol 29 June
I
10 4
661
Dynamic behaviour of pulsed magnets." T. Onishi et al. Table 2
Physical properties of helium and nitrogen
Density Vapour (BP) Liquid (BP) I
t-
Latent heat (BP)
z
He (kg m -3) 17.2 124.8
N2 (kg m -3) 4.59 804.2
He (kJ m -3) 2.61 x103
N2 (kJ m -3) 1.60x10 s
"6 .E
Vo depends on NE6 and Nf, where those are expressed as
o
I
!
!
[
[ I 100
0
Figure 10 0--,5.9T~0
!
I
l
[ I 200
I
t (s) Mass flow of evaporated gas. B m, 5.9T; •m, 4 T s - t ;
tl~....._ [
[
[
[
[
[
I
10001 e-
8 UJ
<
100
i o |
I
100
1
I
2
I
3
I
4
I
5
l
6
7
Time after a shot (rain}
Figure 11
Time dependence of AE counts after a shot
Total counts of the residual AE detected by all the 44 AE sensors after a shot of pulse operation is shown in Figure 11. The number of counts are small compared to those in Figure 9. This is due to the reason why the AE was not counted during a shot of pulse operation. The result indicates that thermal stresses of the windings and their support structures as well as helium bubbles (in a form of very fine sphere, as discussed previously) remain for a long period after a shot 5. Such phenomena will be harmful against improving duty cycle. Discussions
The size of cooling channel of the magnet is not large enough to accommodate all the evaporated helium gas. Therefore, unless the gas in the channel is promptly evacuated to the outside of the magnet, the ratio of liquid helium to gas will be decreased during a pulse operation. We will calculate the flow velocity of the gas under an assumption of the slug flow. G.B. Wallis 6 showed the relationship ~ versus Voo, where V0 is a flow velocity of the slug in a round tube inclining by 0 degree from vertical and Voo is the flow velocity at 0 = 0 and is given as V~o = kx pf- 1 / 2 { g D ( p f - p , ) } x/2
662
Cryogenics 1989 Vol 29 June
(l)
NE6 = gD2(pf -- pg)/a
(2)
N f = gl12 . D312. pf//2f
(3)
g is the gravity constant, D is the tube diameter, p is
density (f:liquid, g: gas), tr is surface tension, a n d / ~ is viscosity. In the case of liquid helium, by substituting tr = 0.093 dyn cm-2, and/~f = 3. 5 x 10-5 Poise into Equations (2) and (3), we obtain NE6 = 283 and Nf = 39500. He showed that for such large values, the surface tension and viscosity will be neglected and then ~ will be rather larger than V® even if 0 = 85 °, that is, the tube inclines only by 5 ° from horizontal. Such a situation will correspond to an inertia dominant case, and k~ in Equation (1) is given as 0.345; we then obtain V~o~ 6 cm s - 1 for D = 0.4 cm. Half a cooling channel length of the magnet is about 11.5 cm, and accordingly it takes about 2 s for evacuation of helium gas in case of slug flow. This means that evaporated gas in the sloped channel will not necessarily be promptly evacuated even in the case of only one shot of pulse operation, and that if the pulse operation is repeated at more than 1 Hz or so, gas will be accumulated in the channel. In 3 MJ magnet, the volume capaciy of the cooling channel is designed to be about the same as the amount of evaporated gas. Therefore, the duty cycle of pulse operation will not increase unless a.c. losses are decreased.
A consideration N 2 cooled coil
of thermal
design
of liquid
Latent heat of liquid nitrogen is large compared to liquid helium, but the volume expansion of the evaporated gas is very much larger than that of helium, as listed in Table 2. Therefore, under an assumption of unit heat input into a magnet, the volume ratio of those evaporated gases, VNJVHc is calculated to be about 0.4 as their boiling points. If nitrogen gas is evacuated in a form of slug flow bubble, the velocity calculated from Equation (1) is approximately the same as that of helium. On the contrary, if it is evacuated in the form of a rigid and fine sphere, the velocity has to be calculated from the following equation 6 V~o = d2 g(pf - pg)/18/~f
(4)
where d is a sphere diameter. For a gas sphere of, for example, 0.1 mm diameter, we obtain V= ~ 2.6 cm s- 1 for nitrogen, while V~ ,~ 16 cm s-~ for helium.
Dynamic behaviour of pulsed magnets: T. Onishi et al. Therefore, fine bubbles of nitrogen gas will be more difficult to evacuate. From these considerations, a.c. losses of such large liquid nitrogen cooled coils as 3 MJ magnet have to be reduced to approximately the same magnitude of the liquid helium cooled one. This means that the filament size of high T~ conductor must be made somewhat finer than expected. As to the stability against transient disturbances, such a large latent heat will be very effective.
Concluding remarks Dynamic and thermal properties of 3 MJ pulsed magnet are described. It is clarified that even for the bath-cooled pulsed magnet, it is stable against 1000 times of pulse operations. It takes a long time for the evacuation of gas evaporated due to a.c. losses. Therefore, for practical application of the equipment such as the power supply, where a repetition frequency will be in the order of 1 Hz or so, it is important to reduce a.c. losses and to design the cooling channel so that gas may be quickly evacuated. Even if the liquid nitrogen cooled superconducting
magnet is realized, the a.c. losses will not be allowed to exceed to an extreme those of the liquid helium cooled magnet from the viewpoint of gas evacuation.
Acknowledgements The authors would like to express their gratitude to Dr K. Koyama for his support and management. They also gratefully acknowledge the collaboration of Mr Y. Katsura of Mitsubishi Electric Company on the measurement of strains.
References 1 Kim, S.H. et al. Proc 9th Syrup Engineering Problems of Fusion Research Chicago (1981) 2 Onishi,T. et M. IEEE Trans Magn (1985) MAG-21 799 3 Shintomi,T. and Masuda, M. Proc of the US-Japan Workshop on Superconductive Energy Storage Madison, USA (1981)442 4 Tateishi, H. etaL Adv Cryo Eng (1986)31 159 5 Nomura,H. et al. Proc of 36th Japanese Cryog~4nicEngineering Conf Kanagawa, Japan (1986)A2-5 6 Wallis, G.B. One-dimensional Two-phase Flow (McGraw-Hill Inc., USA (1969)282
Cryogenics 1989 Vol 29 June
663
Keywords: superconducting magnets; pulsed magnets; repetitive cycling
Pulsed superconducting magnets have been developed for applications to fusion reactors, pulsed energy storage equipments, and so on 1-3. It is essentially important to improve the reliability of withstanding repetitive cycles of pulse operations and the duty cycles in order to make them fit for practical use. However, repetitive operations of magnets have not been studied so far from the viewpoint of fatique. It is also important to consider dynamic behaviour of evaporated gas from the viewpoint of duty cycle. In the present paper, the fatigue properties and helium gas behaviour evaporated due to a.c. losses of the 3 MJ pulsed magnet will be discussed.
the 12 double pancake coils are stacked, it is precompressed by about 400 tons, and then fastened with 16 tie rods. The main parameters of the magnet are listed in Table 1. Strain gauges are attached on the surface of the outer support bands of the central and both end pancake coils of the magnet. Those are schematically shown in Figure 5. Three strain gauges are attached separating each other by 120°. CuNi-clad strand (#O~n).
CuNi ~ ~ " " ~ b a s i c
3 MJ pulsed magnet
strand
Nbli
Structure a n d parameters
The conductor used is a multistage twisted cable as shown in Figure 1. A Normex tape (0.5mm thick, 7 mm wide) is wound on the final cable spirally at an interval of 6 mm. The insulated cable is co-wound with the insulated stainless steel strap with approximately the same width as the cable in a double pancake fashion. A schematic illustration of a completed double pancake coil is shown in Figure 2, and a photograph in Figure 3. The glass fibre reinforced plastic (GFRP) spacer (4 mm thick) is interleaved between the single pancake coils. 3 MJ magnet is fabricated by using 12 double pancake coils. The spacers between the coils are 8 mm thick GFRP. The 100 spacers are assembled in a radial manner on the surface of the windings. The ratio of the spacer width and gap between the spacers is designed to be 2:1. Liquidbubble separating plates with the slope of 3° from horizontal are inserted in the gap as shown in Figure 4. Therefore, the helium bubble will not rise to the upward coils but will be evacuated radially along the plate. After
*Paper presented at the Seminar on Basic Mechanisms of Helium Heat Transfer and Related Stability of Superconducting Magnets, Fukuoka, Japan, 29 August-2 September 1988
evel
K (
level
cable
Figure 1
Schematic of cable cross section
0011-2275/89/060659-05 $03.00 © 1989 8utterworth & Co (Publishers) Ltd
Cryogenics 1989 Vol 29 June
659
Dynamic behaviour of pulsed magnets: T. Onishi et al. He bubble r~
(A-A) Bubble-Sepotoling Double Pancake ~
Spacer
Bubble-llquid separating plate
Figure 4 Axial Suppotl PIole
•2 0 0
mm
430 mm
.I
.
.
.
.
Bubble-liquid separc:ting plate
.
Illustration of liquid-bubble separating plate
,0.4 -V
Oul*r ~porI Bond
.I
Figure 2 Double pancake coil structure.Arrows show flow pattern of helium bubbles
Figure 3
,~ ~'="
f
capacity of the power supply. The load line and operating currents are shown in Figure 6.
Fatigue tests• 3 MJ magnet was operated pulsively in bipolar field sweep modes 4. A typical current waveform is shown in Figure 7. These operations were repeated and the total number of operations amounted to 1000 times in all by regarding one operation as an operation from 0 to a peak current and then to 0. During the repetitive pulse operations, the strains of the windings and the total counts of AE signal were measured. The number of the AE signals were summed up from all the AE sensors (44 sensors) which were attached at the end part (near the outermost turn of the windings) of the spacers between the double pancake coils. The results are shown in Figures 8 and 9. Those figures show that any change of strains did not occur up to 1000 times of pulse operations and the AE counts gradually decreased. The reduction of the total AE counts means that the dominant part of the AE in the present magnet came from the wire motions and accordingly they gradually decreased with increasing repetitive pulse operations. Therefore, the rigidity of the windings is supposed to be improved during the repetitive pulse operations up to 1000 times of operations at least. A maximum strain of approximately 200 p.p.m, was obtained, which was consistent with calculation.
Photograph of double pancake coil
•
ST- 1-3
,;U2/I Table 1
Parameters of 3 MJ pulsed magnet
Coil Winding i.d. Winding o.d. Winding height Total turns Inductance lop Gap,coil BM
12 double pancakes 400 mm 860 mm 625 mm 792 0.2 Henry 5500 A 30.3 A mm -2 6.6T
]:::::::::lt_ . . . . . ] i 1 ~
r'
l .... J~| -
/ll::i
,.%
"I
;I----ill
II]::==:l
~
t~ !
Test results Firstly, the magnet was operated at a low rate of change of magnetic field and generated a maximum field of 6.6 T on the windings at 5500 A without any quenches. Then, in a pulse operation the magnetic fields of about 6.5 T and 6 T were generated at 2.2 T s- x and 4 T s- ~, respectively. These operating currents were limited by the
660
Cryogenics 1989 Vol 29 J u n e
•
30mm 400
mm
922 mm I 0 0 0 mm Figure 5
Position of strain gauges
~/
~'
Ch
Dynamic behaviour of pulsed magnets: T. Onishi et al. 3 MJ Pulsed Magnet 10 200t>~tr~e__o_....~°"~o--...tr.o
Pulse Operation
"
/' 5400 A L 6.48T ~ 2.2Z/sec ~
~
~ BM "t , ~
/ 4950 A ( 5.94T ~ / X k4T/sec-/ /
~
.71
~ ~ -~.
. . . .
/
--
--
~ ST6-2 ~ ST1-3 ~ ST1-1 "-- ST1-2
_
~"-D-2
O
"
I m
5500A(DC) 6.6T
--
~
~
f
\
I
/
I I
/ 3
100
~
'-- ST6-3
,-- SS-1 D-3 .1,42-- -,o-.,~>._o,__0.~_~,__o._I~ ..~ D--4
oJ "--"~-.o,- g.- "~"
RepetitivePulse
Operation
--I00~
~.. ~
,o-- ~. ~- ~
"°'--'°'---o---.--o- "~".o
SB-1
2 ._
o ~ . . . ,,----'----~ .4-. . -~. . . 4,--.,4. . . 4-. . .-~--~-~ ,---SB-11
1
0
0
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
-200
B (T) Figure
< ~J
= E
6
L o a d line a n d o p e r a t i n g c u r r e n t of 3 M J m a g n e t
, MJ•magnet
5910 A(4.54 MJ)
6 5 4 3
t
I
-300 500
>
MJ
n
Figure +4
8
12.09 MJ) 0
1
2
3
4
8
1000
Strains
versus
pulse operations
E
"~
5
\
•
-2
~
-4
~
operation
"1
I
I
T
X
6
Typical current waveform of a bipolar field sweep
-
\
Time (s) 7
900
E Q3
o
0
/
800
m
+2
,agnet
/
700
Number of Pulse Operations
A
<
2
Figure
600
I
,¢ O x E
Thermal characteristics. The evaporated gas due to a.c. losses was measured by a mass flow meter at room temperature• A typical result is shown in Figure 10 which was obtained against a pulse operation (0--* 5.9 T - - , 0 at 4 T s - ~). The mass flow of evaporated gas exists for more than 200 s. As will be discussed later, the evaporated gas will be evacuated in about 2 s when it will be in the form of slug flow, while it takes a period roughly in the order of 100 s for evacuation in case of a very fine sphere of, for example, 10#m in diameter. This indicates that the long period of time required for evacuation shown in Figure 11 may be in part caused by the existence of gas in the form of a very fine sphere. Another reason can be explained by the thermal relaxation time of gas in the cryostat.
LU
< o
t-
r •
10 Figure
9
102
10 3
. t ....
Pulse operation Times Total AE counts v e r s u s pulse operation times
Cryogenics 1989 Vol 29 June
I
10 4
661
Dynamic behaviour of pulsed magnets." T. Onishi et al. Table 2
Physical properties of helium and nitrogen
Density Vapour (BP) Liquid (BP) I
t-
Latent heat (BP)
z
He (kg m -3) 17.2 124.8
N2 (kg m -3) 4.59 804.2
He (kJ m -3) 2.61 x103
N2 (kJ m -3) 1.60x10 s
"6 .E
Vo depends on NE6 and Nf, where those are expressed as
o
I
!
!
[
[ I 100
0
Figure 10 0--,5.9T~0
!
I
l
[ I 200
I
t (s) Mass flow of evaporated gas. B m, 5.9T; •m, 4 T s - t ;
tl~....._ [
[
[
[
[
[
I
10001 e-
8 UJ
<
100
i o |
I
100
1
I
2
I
3
I
4
I
5
l
6
7
Time after a shot (rain}
Figure 11
Time dependence of AE counts after a shot
Total counts of the residual AE detected by all the 44 AE sensors after a shot of pulse operation is shown in Figure 11. The number of counts are small compared to those in Figure 9. This is due to the reason why the AE was not counted during a shot of pulse operation. The result indicates that thermal stresses of the windings and their support structures as well as helium bubbles (in a form of very fine sphere, as discussed previously) remain for a long period after a shot 5. Such phenomena will be harmful against improving duty cycle. Discussions
The size of cooling channel of the magnet is not large enough to accommodate all the evaporated helium gas. Therefore, unless the gas in the channel is promptly evacuated to the outside of the magnet, the ratio of liquid helium to gas will be decreased during a pulse operation. We will calculate the flow velocity of the gas under an assumption of the slug flow. G.B. Wallis 6 showed the relationship ~ versus Voo, where V0 is a flow velocity of the slug in a round tube inclining by 0 degree from vertical and Voo is the flow velocity at 0 = 0 and is given as V~o = kx pf- 1 / 2 { g D ( p f - p , ) } x/2
662
Cryogenics 1989 Vol 29 June
(l)
NE6 = gD2(pf -- pg)/a
(2)
N f = gl12 . D312. pf//2f
(3)
g is the gravity constant, D is the tube diameter, p is
density (f:liquid, g: gas), tr is surface tension, a n d / ~ is viscosity. In the case of liquid helium, by substituting tr = 0.093 dyn cm-2, and/~f = 3. 5 x 10-5 Poise into Equations (2) and (3), we obtain NE6 = 283 and Nf = 39500. He showed that for such large values, the surface tension and viscosity will be neglected and then ~ will be rather larger than V® even if 0 = 85 °, that is, the tube inclines only by 5 ° from horizontal. Such a situation will correspond to an inertia dominant case, and k~ in Equation (1) is given as 0.345; we then obtain V~o~ 6 cm s - 1 for D = 0.4 cm. Half a cooling channel length of the magnet is about 11.5 cm, and accordingly it takes about 2 s for evacuation of helium gas in case of slug flow. This means that evaporated gas in the sloped channel will not necessarily be promptly evacuated even in the case of only one shot of pulse operation, and that if the pulse operation is repeated at more than 1 Hz or so, gas will be accumulated in the channel. In 3 MJ magnet, the volume capaciy of the cooling channel is designed to be about the same as the amount of evaporated gas. Therefore, the duty cycle of pulse operation will not increase unless a.c. losses are decreased.
A consideration N 2 cooled coil
of thermal
design
of liquid
Latent heat of liquid nitrogen is large compared to liquid helium, but the volume expansion of the evaporated gas is very much larger than that of helium, as listed in Table 2. Therefore, under an assumption of unit heat input into a magnet, the volume ratio of those evaporated gases, VNJVHc is calculated to be about 0.4 as their boiling points. If nitrogen gas is evacuated in a form of slug flow bubble, the velocity calculated from Equation (1) is approximately the same as that of helium. On the contrary, if it is evacuated in the form of a rigid and fine sphere, the velocity has to be calculated from the following equation 6 V~o = d2 g(pf - pg)/18/~f
(4)
where d is a sphere diameter. For a gas sphere of, for example, 0.1 mm diameter, we obtain V= ~ 2.6 cm s- 1 for nitrogen, while V~ ,~ 16 cm s-~ for helium.
Dynamic behaviour of pulsed magnets: T. Onishi et al. Therefore, fine bubbles of nitrogen gas will be more difficult to evacuate. From these considerations, a.c. losses of such large liquid nitrogen cooled coils as 3 MJ magnet have to be reduced to approximately the same magnitude of the liquid helium cooled one. This means that the filament size of high T~ conductor must be made somewhat finer than expected. As to the stability against transient disturbances, such a large latent heat will be very effective.
Concluding remarks Dynamic and thermal properties of 3 MJ pulsed magnet are described. It is clarified that even for the bath-cooled pulsed magnet, it is stable against 1000 times of pulse operations. It takes a long time for the evacuation of gas evaporated due to a.c. losses. Therefore, for practical application of the equipment such as the power supply, where a repetition frequency will be in the order of 1 Hz or so, it is important to reduce a.c. losses and to design the cooling channel so that gas may be quickly evacuated. Even if the liquid nitrogen cooled superconducting
magnet is realized, the a.c. losses will not be allowed to exceed to an extreme those of the liquid helium cooled magnet from the viewpoint of gas evacuation.
Acknowledgements The authors would like to express their gratitude to Dr K. Koyama for his support and management. They also gratefully acknowledge the collaboration of Mr Y. Katsura of Mitsubishi Electric Company on the measurement of strains.
References 1 Kim, S.H. et al. Proc 9th Syrup Engineering Problems of Fusion Research Chicago (1981) 2 Onishi,T. et M. IEEE Trans Magn (1985) MAG-21 799 3 Shintomi,T. and Masuda, M. Proc of the US-Japan Workshop on Superconductive Energy Storage Madison, USA (1981)442 4 Tateishi, H. etaL Adv Cryo Eng (1986)31 159 5 Nomura,H. et al. Proc of 36th Japanese Cryog~4nicEngineering Conf Kanagawa, Japan (1986)A2-5 6 Wallis, G.B. One-dimensional Two-phase Flow (McGraw-Hill Inc., USA (1969)282
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